The lock takes over the armband from injured number eight Bobby Skinstad, who replaced regular leader John Smit and vice-captain Victor Matfield, who were rested.
Veteran Jacques Cronje takes Skinstad's place in the team, while Muller partners Albert van den Berg in the second row.
Bismarck du Plessis and Jaco Pretorius come into the side at hooker and wing respectively, replacing Gary Botha and Bevan Fortuin from the 25-17 loss in Australia last Saturday.
Du Plessis joins his brother, prop Jannie, in the starting line-up of a Test for the first time, while JP Pietersen shifts to full-back to accommodate Pretorius.
South Africa: JP Pietersen; Breyton Paulse, Waylon Murray, Wynand Olivier, Jaco Pretorius; Derick Hougaard, Ruan Pienaar; CJ van der Linde, Bismarck du Plessis, Jannie du Plessis; Albert van den Berg, Johann Muller (captain); Wikus van Heerden, Pedrie Wannenburg, Jacques Cronje.
Replacements: Gary Botha, Eddie Andrews, Gerrie Britz, Hilton Lobberts, Michael Claassens, Peter Grant, Tonderai Chavhanga.